Frequency responses of streamwise-constant perturbations in channel flows of Oldroyd-B fluids

Content Provider	Semantic Scholar
Author	Vi, Ć.
Copyright Year	2009
Abstract	Non-modal amplification of disturbances in streamwise-constant channel flows of OldroydB fluids is studied from an input-output point of view by analyzing the responses of the velocity components to spatio-temporal body forces. These inputs into the governing equations are assumed to be harmonic in the spanwise direction and stochastic in the wall-normal direction and in time. An explicit Reynolds number scaling of frequency responses from different forcing to different velocity components is developed, showing the same Re-dependence as in Newtonian fluids. It is found that some of the frequency response components peak at non-zero temporal frequencies. This is in contrast to Newtonian fluids, where peaks are always observed at zero frequency, suggesting that viscoelastic effects introduce additional timescales and promote development of flow patterns with smaller time constants than in Newtonian fluids. The temporal frequencies, corresponding to the peaks in the components of frequency response, decrease with an increase in viscosity ratio (ratio of solvent viscosity to total viscosity) and show maxima for nonzero elasticity number. Our analysis of the Reynolds-Orr equation demonstrates that the energy-exchange term involving the streamwise/wall-normal polymer stress component τxy and the wall-normal gradient of the streamwise velocity ∂yu becomes increasingly important relative to the Reynolds stress term as the elasticity number increases, and is thus the main driving force for amplification in flows with strong viscoelastic effects.
File Format	PDF HTM / HTML
Alternate Webpage(s)	http://arxiv.org/pdf/0901.2175v1.pdf
Language	English
Access Restriction	Open
Subject Keyword	Arabic numeral 0 Assumed Elasticity (data store) Flow Frequency response Gradient Image scaling Liquid substance Maxima Modal logic Normal (geometry) Polymer Reynolds-averaged Navier–Stokes equations Small Test scaling Velocity (software development)
Content Type	Text
Resource Type	Article